Dynamic network DEA approach with diversification to multi-period performance evaluation of funds

When analyzing the relative performance of mutual funds, current data envelopment analysis (DEA) models with diversification ignore the performance change in consecutive periods or the dynamic dependence among investment periods. This paper introduces a novel multi-period network DEA approach with diversification and directional distance function. The new approach decomposes the overall efficiency of a mutual fund in the whole investment interval into efficiencies at individual periods. At each period, mutual funds consume exogenous inputs and intermediate products produced from the preceding period to produce exogenous outputs and intermediate products for the next period to use. Efficiency decomposition reveals the time at which the inefficiency occurs. The new model can provide expected inputs, outputs and intermediate variables at individual periods, which are helpful for managers to find factors causing the overall inefficiency of a fund. Under the assumption of discrete return distributions and a proper choice of inputs, outputs and intermediate variables, the proposed models can be transformed into linear programs. The applicability and reasonability of the proposed method are demonstrated by applying it to assess the relative performance of funds in Chinese security market and European security market, respectively.